Peritrochoid Formulae How to implement these formulae in Solidworks so they are smart models?
1. Rotor Housing
Inner Surface
X = e cos α + R cos (α/3) + a cos ((α/3)+φ)
Y = e sin α + R sin (α/3) + a sin ((α/3)+φ)
e = 19
R = 130
a = 3
φ = 26.2
2. Rotor
X = R cos 2v + (3/2)(e^2/R)(cos 8v - cos 4v)
+/- e(cos 5v + cos v)(1-(9e^2/R^2)sin^2 3v)^(1/2)
+/- (3/2)(ea’/R)(cos 5v - cos v)
+ a’ cos 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)
Y = R sin 2v + (3/2)(e^2/R)(sin 8v + sin 4v)
+/- e(sin 5v + sin v)(1-(9e^2/R^2)sin^2 3v)^(1/2)
+/- (3/2)(ea’/R)(sin 5v + sin v)
+ a’ sin 2v (1-(9e^2/R^2)sin^2 3v)^(1/2)
These functions are cyclic functions with the period of 2π.
The inner envelope corresponds to:
v = (1/6)π ~ (1/2)π, (5/6)π ~ (7/6)π, (3/2)π ~ (11/6)π
Generally a’ can be determined as follows:
a’ = a - Sp
where
a: amount of parallel transfer of trochoid
Sp: minimum clearance between rotor and rotor housing
SolidworksEducator / Student